Casimir wormholes in $$2+1$$ dimensions with applications to the graphene

Abstract In this paper we show that wormholes in (2+1) dimensions (3-D) cannot be sourced solely by both Casimir energy density and tension, differently from what happens a 4-D scenario, which case it has been shown recently, the direct computation of exact shape redshift functions wormhole solution, is possible. We 3-D spacetime same not true since arising at least an event horizon inevitable. do analysis for massive massless fermions, as well scalar fields, considering quasi-periodic boundary conditions find possibility to circumvent such restriction introduce, besides cosmological constant, embedding surface manifold applying perpendicular weak magnetic field. This causes additional tension on it, contributes formation wormhole. Finally, discuss producing condensed matter analogous graphene sheet analyze electronic transport through it.